Ramsey was particularly pleased with the way the players responded
from the disappointment of their last-gasp 2-1 defeat to England, who
had to settle for second place in the group after a toothless goalless
draw with Slovakia.
"We wanted to come to this competition and really make a statement,
put Welsh football on the map and show what we are capable of doing. I
think we've done that," he told ITV.
"Maybe against England we let the occasion get to us a bit, in terms
of when we had the ball. That was something we really wanted to improve
on [against Russia].
"We've
shown what a good defensive team we are, but now we have shown what a
good team we are in possession. We created loads of opportunities and we
can really be proud of what we have achieved so far."
For only the second time in their history, Wales are through to the knockout stages of a major international tournament.
They do not yet know the identity of last-16 opponents, although they
are certain to face a third-placed team from either Group A, C or D in
Paris on Saturday.
"That was our main target - to get out of the group," Ramsey added. "We've achieved that and finished top.
"It’s a great day for Welsh football. I've been waiting for a while
for this moment, to show what we are capable of on a big stage.
"Who knows what can happen now?"